Let E be an ample vector bundle of rank n-2 on a complex projective manifold X of dimension n, having a section whose zero locus is a smooth surface Z. Pairs (X,E) as above are classified under the assumption that Z is a P^1-bundle over a smooth curve. We also prove that X has negative Kodaira dimension if, in a similar setting, Z is a birationally ruled surface.
Geometrically ruled surfaces as zero loci of ample vector bundles / A. Lanteri, H. Maeda. - In: FORUM MATHEMATICUM. - ISSN 0933-7741. - 9:1(1997), pp. 1-15.
Geometrically ruled surfaces as zero loci of ample vector bundles
A. LanteriPrimo
;
1997
Abstract
Let E be an ample vector bundle of rank n-2 on a complex projective manifold X of dimension n, having a section whose zero locus is a smooth surface Z. Pairs (X,E) as above are classified under the assumption that Z is a P^1-bundle over a smooth curve. We also prove that X has negative Kodaira dimension if, in a similar setting, Z is a birationally ruled surface.
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